This Widget will display the YouTube videos that you want and the only data needed are the video URLs. There is no need to get YouTube API.
You have to give write permissions to
/wp-content/plugins/berri-youtube-gallery/images/ directory, configure the gallery in the widget panel and save configuration.
Have you the requirements? You must have widget enabled, a widgetized theme, PHP GD Library installed and
allow_url_fopen option enabled.